Electronic structure of superconducting multilayers

The Bloch waves, the energy bands, and the local and global densities of states are computed for superconducting multilayers in which the Fermi energy in the superconducting (S) layers, ${\mathrm{\varepsilon }}_{\mathrm{FS}}$, may exceed the one in the normal (N) layers, ${\mathrm{\varepsilon }}_{\mathrm{FN}}$. Self-consistent pair potentials and their equivalent square-well representations are considered. If the S-layer thickness exceeds several coherence lengths the densities of states exhibit the subgap peak (besides the BCS peak) and the Tomasch-McMillan-Anderson oscillaitons known from SNS junctions. These features, due to off-diagonal (Andreev) scattering, decrease with increasing ratio ${\mathrm{\varepsilon }}_{\mathrm{FS}}$/${\mathrm{\varepsilon }}_{\mathrm{FN}}$ because of the competition from diagonal scattering. The temperature dependence of the energetic position of the subgap peak is weaker than that of the BCS peak. In multilayers with S-layer thickness of the order of magnitude of one coherence length and ${\mathrm{\varepsilon }}_{\mathrm{FS}}$/${\mathrm{\varepsilon }}_{\mathrm{FN}}$≫1, the local density of states is BCS-like in the S layers and normal-metal-like in the N layers. This is due to electron localization in the S layers and consistent with recent scanning tunneling microscope conductance measurements in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$.